Want to find out what is known about any particular gene? Here's a good place to start. -
Entrez Gene This is probably my favourite starting point for finding out about a new gene of interest and has handy links to most of the references and sequence information.

Want to find a piece of peer-reviewed scientific research? Want to check the references from an article, or look up the publication record of an expert quoted in a newspaper or blog piece? Try this database. It will give you the abstract (outline) of every paper and will link to the full thing and tell you which articles are free and open-access. -
NCBI's PubMed All newly published research is quickly added to this site.

Want to be able to decode DNA? This is how DNA codes for protein, and is, to my eyes, a thing of beauty. -
The Genetic Code (presented here as RNA. For DNA, simply replace the U's with T's (Uracil with Thymine)).